A parking lot is given by the diagram below. Find the perimeter of the parking lot in terms of x.

Question

Answer 1

add up the sides = (x^2 -12x +10) + (4x+1)+ (x^2 -x -16) + (3x+12) + 5x + (6x-14) +(x^2 -10x-17)+(x^2-3x-12)

= 4x^2 -7x -44= perimeter

combine like terms

only "tricks" to the question is getting the last 6 terms (x^2 -10x-17) and Just take the right side height and subtract the two left side segments x^2-x-16 - 5x -(4x+1) = x^2 -x-5x-4x -16-1 - x^2 -10x -17

and also find the missing horizontal section: take (x^2-12x -10) and subtract (6x-14) and (3x+12)

x^2 -12x-10 -6x+14-3x-12 = x^2 -3x-12

the rest is tedious arithmetic, where a mistake can easily creep in, somewhere

x^2 +x^2 +x^2+x^2 = 4x^2

-12x +4x -x +3x +5x +6x -10x-3x = (-12+4-x+3+5+6-10-3)x = -7x

10+1-16+4 -14-17-12= -44

Answer 2

The perimeter is the sum of all the sides of the parking lot. It appears from the diagram that two sides are not given. If the diagram can be considered to be steps, the horizonatal portion of the first step and the vertical portion leading to the second step are not given. The missing dimensions can be obtained by subtracting the sum of the known horizontal sections from the total length given at the bottom of the diagram. Similarly, the unknown vertical section can be obtained by subtracting the sum of the known vertical sections from the total vertical section given at the right side of the diagram.

To get the perimeter, add all the individual sections and simplify the expression by collecting like terms. This will give a polynomial having X^2, X, and constant terms.